INDEX 393partial ordering, 227,245
range of, 233
reflexive, 232
static view of, 231
subset, 232,246
symmetric, 232
transitive, 232
well-defined, 250
Relative complement, 19, 219
Relative maximum of a function, 74, 99,
101,211
Relative minimum of a function, 99
Remainder, 239
Removable discontinuity, 130
Representative of an equivalence class,
228, 344
Restriction of a mapping, 258, 260
Right cancellation property of composition,
266,267,268
Right continuous, 144
Right-hand limit, 143,202
Ring, 1 16, 346
commutative, 346
with unity, 346
Rolle's theorem, 22 1
Roster method, 4
Rule method, 5
Rule of correspondence, 253
Russell's Paradox, 3, 15
Sandwich theorem, 202
Schroeder-Bernstein theorem, 276, 285, 289
Second induction principle, 341, 342, 343
Sequence
Cauchy, 203,329, 330, 353,354
cluster point of, 203, 220
convergent, 191,203, 353
limit of, 191, 203
null, 355, 360
Set(s), 3-51
algebra of, 16, 29
bounded, 21 1,220; 246,3 1 1
bounded above, 217,220,246,311
bounded below, 220,246, 31 1
cardinality of, 127, 252, 277-289
cartesian product of, 22, 228, 229
closed, 201, 211, 212
compact, 211,223
complement of, 18,25
convex, 169,200, 21 1
countable, 283
countably infinite, 281, 283, 289
cross product of, 22
denumerable, 283
description method of defining, 5
difference of, 19, 25
disjoint, 17, 28
element of, 4
empty, 9, 36-37, 120-122
equality of, 10, 15, 116
finite, 5, 6, 211, 279, 288
inductive, 185
infinite, 5, 6, 279, 288
intersection of, 16
linearly ordered, 248
mutually disjoint, 28
nonempty, 9
number of elements of a finite, 43
numerically equivalent, 269, 288
open, 191, 194, 201
operations on, 15-23
partially ordered, 245
partition of, 240
pattern method of defining, 6, 14
power, 13
proper subset of, 12, 165, 169
relations between, 228, 230
relative complement of, 19
roster method of defining, 4
rule method of defining, 5
singleton, 9
subset of, 11, 116, 160, 211, 231
superset of, 11
symmetric difference of, 20
totally ordered, 248
truth, 82, 83, 87
uncountable, 283
union of, 16, 25
universal, 6, 36-37
well defined, 4, 14
Set-builder notation, 5
Sheffer stroke, 76
Similar triangles, 240
Simple statement, 55
Simplification, see Law of simplification
Singleton set, 9
Skew lines, 240
Solution set, 6
Specialization, 122, 167, 170, 171-172,
174-177, 179, 198,220
Square matrix, 158, 177
Square root, 110, 303
Statement, 52, 53
compound, 52, 55
of equivalence, 42. See also Logical
equivalence
of implication, 42. See also Logical
implication